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Old 2003-06-24, 19:42   #2
NickGlover
 
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Aug 2002
Richland, WA

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Correct me if I'm wrong, but before you even consider whether O6 can touch O1, the existing arrangement you have given is not planar. If you represent the sides of the triangle and the circles as nodes in a graph and try to connect them all, you can see this.

Also consider it like this: How can both O1 and O4 touch AB and AC and both have a clear path for O1 to touch O2 and O4 to touch O3? No matter how you try to arrange it, one circle in each angle has to completely block the other from touching any other circles.
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